The phenomenon of memorization and generalization can be quantified by the leave-one-out influence function [1]}, [2]}, which measures the influence of example \(\mathbf {z}_i\)  to the prediction of \(\mathbf {z}_{target}\) .
Let \(f_{\mathcal {D}}\)  be the model trained on the full training dataset \(\mathcal {D}\)  and \(f_{\mathcal {D}\backslash \lbrace \mathbf {z}_{i}\rbrace }\)  be the model trained on \(\mathcal {D}\)  excluding example \(\mathbf {z}_i\) , then the influence is defined as:
\( \mathcal {I}(\mathbf {z}_{target}, \mathbf {z}_{i} ; \mathcal {D}) :=\mathcal {L}(f_{\mathcal {D}\backslash \lbrace \mathbf {z}_{i}\rbrace }, \mathbf {z}_{target})- \mathcal {L}(f_{\mathcal {D}}, \mathbf {z}_{target}) \,,\) 
